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- Jan 26, 2012

- 995

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**Problem**: Let $f$ be function with measurable domain $D$. Show that $f$ is measurable if and only if the function $g$ defined on $\mathbb{R}$ by $g(x) = \begin{cases}f(x) & x\in D\\ 0 & x\notin D\end{cases}$ is measurable.

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